Grice on "α ∈ β" (WoW:VI:133n1) -- repr. in Searle and scaring Chomsky

--- by JLS
------- for the GC

THIS IS TO REPLY, in part, Andy's acute question in his comment to "Truly understood":

How are the concepts to which
the uppercase words refer actually represented?

I pointed out that Grice will NOT engage in this silly practice, and use rather, if he must ('must' understood in the preterite, here -- no such trick in English), by variables, using the more distinguished phi and khi, or alpha, alpha', beta, and beta', as in the footnote referred to in title which scared Chomsky when he read it in Searle, "The philosophy of language" (Oxford, 1971) and which him fodder for his boring 3rd lecture against Grice at Oxford (The Locke Lectures).

----

"α ∈ β"

----

So Grice wants to just stick with any 'feature' that belongs to an 'item'.

We have four features in his long shaggy-dog story:

the dog that Jones calls 'Fido' -- alpha
the dog that Jones owns ----------- alpha'
shaggy ---------------------------- beta
hairy-coated ---------------------- beta'

---

When we think of co-extensionality of features, we mean that all items which have feature beta, also have feature beta' (All shaggy things are hairy-coated things). We are concerned with Grice on 'beta', here because for the sub-mechanism of referring the logic is slightly different from the more basic sub-mechanism of 'predicating'.

So what that 'infamous' footnote that does display Grice as the extensionalist he once was reads:

"The definiens suggested for
explicit correlations is, I think,
insufficient as it stands."

To see that Grice managed Harvard University Press to have this as a footnote is miraculous. He goes on in same self footnote:

"I would not wish to say that if
A deliberately detaches B from
a party, he has thereby correlated
himself with B, nor that
a lecturer who ensures that just
ONE blackboard is visible to
EACH member of his audience (and to
no one else) has thereby
explicitly correlated the blackboard
with EACH member of the audience,
even though in each case the
analogue of the suggested
defininens is satisfied."

--- His ability to bring in the most disparate illustrations is just genial. It brings the whole abstract field he is plowing into something that even the dullest student or reader should understand. It's like he is saying: 'No way you can defend yourself by saying that I did use convoluted examples.' He goes on:

"To have explicitly correlated X
with EACH MEMBER [i.e. each ITEM that
is a member. JLS] of a set K, not
only must I have intentionally effected
that a particular relation R
holds between X and all those (and
only those) items which belong to
K [feature. JLS], but also my
purpose or end in setting up this
relationship must have been to perform
an act."

---- Imagine if you wanted to say this -- of such an importance -- in just a footnote!

He goes on:

"... to perform an act as a result
of which there will be some relation
or other which holds between X and
all those (and only those) things [or
items. JLS] which belong
to K."

And here is the important bit, where he plays Zermelo-Fraenkel:

"To the definiens, then, we would ADD, within
the scope of the initial quantifier, the
following clause."

And what does the clause look like? It looks LIKE this. In fact it IS this:

& U's purpose in effecting
that (x) (......) [six dots. JLS] is that (ER') (z)(R' 'shaggy'z <-> z ∈ y (sc. y is hairy-coated)).

Crystal clear, right?

To understand him fully we need to expand on the NEED of this footnote, but I bring it to the forum because it's the ONLY place (surely for abbreviatiory purposes) that Grice cares to use that rather infamous concept, ∈, that he will later criticise when he sees "Extensionalism" as a bête noire. Of course he KNEW he wasn't an extensionalist (enemy of intenSions) even then, because he IS using at least intenTional terms (like 'end' or 'purpose'), and he is well aware of the problems of quantifying in:

"I [did say] at one point that
intenSionality seems to be embedded
in the very foundations of the
theory of language"

He allows, though, that

"it may be possible to derive
... the intenSional concepts
which I have been using from
more primitive EXTENSIONAL
concepts." (WoW:137)

Etc.